Scatter correction

Note that this relationship is in conPadiction to the well known equation for the calculation of the thickness resolving power given by Halmshaw in 111. The relationship in 111 requires explicit knowledge about built-up factors for scatter correction and the film contrast factory (depending on D) and is only valid for very small wall thickness changes compared to the nominal wall thickness. 

It is possible to make elastic scattering corrections to the algorithm (24) in the case of an Einstein phonon spectrum and purely local exciton-phonon coupling. If we calculate the energy of the polaron state at the value E ss nuio only the matrix elements 5 " should be considered in Eqs.(16). In this case... 

Using Eqs. (29) and (30) we obtain that the coherent potential v i with elastic scattering correction is determined by the following equations... 

Artifact removal and/or linearization. A common form of artifact removal is baseline correction of a spectrum or chromatogram. Common linearizations are the conversion of spectral transmittance into spectral absorbance and the multiplicative scatter correction for diffuse reflectance spectra. We must be very careful when attempting to remove artifacts. If we do not remove them correctly, we can actually introduce other artifacts that are worse than the ones we are trying to remove. But, for every artifact that we can correctly remove from the data, we make available additional degrees-of-freedom that the model can use to fit the relationship between the concentrations and the absorbances. This translates into greater precision and robustness of the calibration. Thus, if we can do it properly, it is always better to remove an artifact than to rely on the calibration to fit it. Similar reasoning applies to data linearization. 

Another popular form of data pre-processing with near-infrared data is the application of the Multiplicative Scatter Correction (MSC, [28]). It is well known that particle size distribution of non-homogeneous powders has an overall effect on the spectrum, raising all intensities as the average particle size increases. Individual spectra x, are approximated by a general offset plus a multiple of a reference spectrum, z. 

W.R. Hruschka, Data analysis wavelength selection methods, pp. 35-55 in P.C. Williams and K. Norris, eds. Near-infrared Reflectance Spectroscopy. Am. Cereal Assoc., St. Paul MI, 1987. P. Geladi, D. McDougall and H. Martens, Linearization and scatter-correction for near-infrared reflectance spectra of meat. Appl. Spectrosc., 39 (1985) 491-500. 

We would like to thank the beamline scientists of ID 15 of the ESRF. T. Buslaps, V. Honkimaki, A. Shukla and P. Suortti for their valuable help with the measurements and F. Maniawski and J. Kwiatkowska for their help with the sample preparation. We are also grateful to J. Felsteiner for sending us his Monte-Carlo simulation program for the multiple scattering correction. 

Fig Variation of asymmetric scattering correction with size factor X, VY or Z. 

Geladi, P., MacDougall, D., Martens, H. Appl. Spectrosc. 39, 1985, 491-500. Linearization and scatter-correction for NIR reflectance spectra of meat. 

Helland, I. S., Naes, T., Isaksson, T. Chemom. Intell. Lab. Syst. 29, 1995, 233-241. Related versions of the multiplicative scatter correction method for preprocessing spectroscopic data. 

Naes, T., Isaksson, T., Kowalski, B. R. Anal. Chem. 62, 1990, 664—673. Locally weighted regression and scatter correction for near-infrared reflectance data. 

MSC Multiplicative signal/scatter correction (preprocessing of NIR data)... 

N.B. Gallagher, T.A. Blake, P.L. Gassman, Application of extended inverse scatter correction to mid-infrared reflectance spectra of soil, J. Chemom., 19, 271 (2005). 

J.L. Ilari, H. Martens and T. Isaksson, Determination of particle size in powders by scatter correction in diffuse near infrared reflectance, Appl. Spectrosc., 42, 722-728 (1988). 

MSC multiplicative scatter correction, bootstrap error-adjusted single-... 

Figure 3.21. Near-infrared reflectance spectra of solid polymer samples before a) and after (b) preprocessing using multiplicative scatter correction.

Martin et al. [102] reported a study in which LIBS was applied for the first time to wood-based materials where preservatives containing metals had to be determined. They applied PLS-1 block and PLS-2 block (because of the interdependence of the analytes) to multiplicative scattered-corrected data (a data pretreatment option of most use when diffuse radiation is employed to obtain spectra). They authors studied the loadings of a PCA decomposition to identify the main chemical features that grouped samples. Unfortunately, they did not extend the study to the PLS factors. However, they analysed the regression coefficients to determine the most important variables for some predictive models. 

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